Question

If BD bisects angle ABC, measure of DBC = 79 degrees, and measure of angle ABC= 9x-4, find the value of x.

Answer 1

Try this option:

answer is 18.

For more information see the attached picture.

Answer 2

Answer:  18

Step-by-step explanation:

Given :  BD bisects angle ABC, measure of DBC = 79 degrees  ---(1), and measure of angle ABC= 9x-4.   (3)

We know that if a line bisects an angle then it means that it is dividing the angle into two equal parts.

So from the given question, we have

$\angle{DBC}=\angle{DBA}=\dfrac{\angle{ABC}}{2}$         (2)

From (1) and (2), we have

$\dfrac{\angle{ABC}}{2}=79^{\circ}$

i.e. ${\angle{ABC}=2\times79=158^{\circ}$

From (3), we have

$9x-4=158\\\\\Rightarrow\ 9x=162\\\\\Rightarrow\ x=\dfrac{162}{9}=18$

Hence, the value of x = 18.